en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of arcsec(e^{3x})

Solution

\frac{d}{d x} (arcsec (e^{3 x}))

Solution

\frac{3}{e ^{6 x} - 1}

Solution steps

\frac{d}{d x} (arcsec (e^{3 x}))

Apply the chain rule:

\frac{1}{( e ^{3 x} ) ^{2} ( e ^{3 x} ) ^{2} - 1} \frac{d}{d x} (e^{3 x})

= \frac{1}{( e ^{3 x} ) ^{2} ( e ^{3 x} ) ^{2} - 1} \frac{d}{d x} (e^{3 x})

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

= \frac{1}{( e ^{3 x} ) ^{2} ( e ^{3 x} ) ^{2} - 1} e^{3 x} \cdot 3

Simplify

\frac{1}{( e ^{3 x} ) ^{2} ( e ^{3 x} ) ^{2} - 1} e^{3 x} \cdot 3 : \frac{3}{e ^{6 x} - 1}

= \frac{3}{e ^{6 x} - 1}

Popular Examples

y^'=(sec(y))/((x+2)^2)

y^{^{'}} = \frac{sec ( y )}{( x + 2 ) ^{2}}

tangent of f(x)=-3+(x+4)^2,\at x=-5 tangent of

f (x) = - 3 + (x + 4)^{2}, at x = - 5

inverse oflaplace (2*(s^2+1))/(s^4)inverse laplace

\frac{2 \cdot ( s ^{2} + 1 )}{s ^{4}}

derivative of e^{(x^2/(2a)})

\frac{d}{d x} (e^{\frac{x ^{2}}{2 a}})

y^{^{'}} = y^{2} - 8

Frequently Asked Questions (FAQ)

What is the derivative of arcsec(e^{3x}) ?
The derivative of arcsec(e^{3x}) is 3/(sqrt(e^{6x)-1)}
What is the first derivative of arcsec(e^{3x}) ?
The first derivative of arcsec(e^{3x}) is 3/(sqrt(e^{6x)-1)}